Malcolm McDowell's eyes were anesthetized for the torture scenes so that he would film for periods of time without too much discomfort. Nevertheless his corneas got repeatedly scratched by the metal lid locks.
The doctor standing over Alex as he is being forced to watch violent films was a real doctor, ensuring that Malcolm McDowell's eyes didn't dry up.
Alex performing "Singing in the Rain" as he attacks the writer and his wife was not scripted. Stanley Kubrick spent four days experimenting with the scene, finding it too conventional. Eventually he approached Malcolm McDowell and asked him if he could dance. They tried the scene again, this time with McDowell dancing and singing the only song he could remember. Kubrick was so amused that he bought the rights to "Singing in the Rain" for $10,000 (about $76,500 in 2022).
Alex "popping" his mouth open for food was entirely improvised, as Stanley Kubrick got incredibly bored during the scene and Malcolm McDowell started acting silly just to keep everyone's attention focused.
Korova Milk Bar is named after the Russian word for cow. Moloko (written on the wall) means milk. The bar's sculptures were based on the work of sculptor Allen Jones. Stanley Kubrick had the milk dispensers emptied, washed and refilled every hour, as the milk curdled under the studio lights. The chairs in the bar were the reupholstered and recycled chairs from the space station in Kubrick's "2001: A Space Odyssey " (1968).
Stanley Kubrick: [eyes] Alex's cuff links are bloody eyeballs, and his own eyes are emphasized throughout his "cure."